Subgroup weight generation based on shielded pin-cell cross section conservation

A method for generating subgroup weights is presented employing the idea of conserving resonance shielded cross sections for representative pin cells. Consistency in the generation and usage steps of the subgroup weights is imposed in a subgroup formulation involving the subgroup fixed source problem to resolve the subgroup level and space dependent self shielding. Consequently, the subgroup level dependent background cross sections are determined and used in the generation step. The requirement of reconstructed cross section error minimization forms a constrained least square problem which is solved by the Lagrange multiplier technique augmented with a regularization term introduced to enhance solution stability. The generated subgroup weights are verified by analyzing various pin cell benchmark problems and comparing with corresponding Monte Carlo solutions. The results for the Rowlands and Mosteller Doppler-effect benchmark problems show small errors of 0.1% in the resonance cross sections and about 70 pcm in multiplication factor, and also good agreement in the reactivity vs. fuel temperature behavior. The problem of the slight over-prediction of the fuel temperature coefficients is noted and discussed as well.